Browsing by Author "Huang, B. J."

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Localization-delocalization transition in Hessian matrices of topologically disordered systems
(2009-04-01)
Huang, B. J.
;
Wu, Ten-Ming
;
物理研究所
;
Institute of Physics
Using the level-spacing (LS) statistics, we have investigated the localization-delocalization transitions (LDTs) in Hessian matrices of a simple fluid with short-ranged interactions. The model fluid is a prototype of topologically disordered systems and its Hessian matrices are recognized as an ensemble of Euclidean random matrices with elements subject to several kinds of constraints. Two LDTs in the Hessian matrices are found, with one in the positive-eigenvalue branch and the other in the negative-eigenvalue one. The locations and the critical exponents of the two LDTs are estimated by the finite-size scaling for the second moments of the nearest-neighbor LS distributions. Within numerical errors, the two estimated critical exponents are almost coincident with each other and close to that of the Anderson model (AM) in three dimensions. The nearest-neighbor LS distribution at each LDT is examined to be in a good agreement with that of the AM at the critical disorder. We conclude that the LDTs in the Hessian matrices of topologically disordered systems exhibit the critical behaviors of orthogonal universality class.
Multifractality of instantaneous normal modes at mobility edges
(2010-11-29)
Huang, B. J.
;
Wu, Ten-Ming
;
物理研究所
;
Institute of Physics
In terms of the multifractal analysis, we investigate the characteristics of the instantaneous normal modes (INMs) at two mobility edges (MEs) of a simple fluid, where the locations of the MEs in the INM spectrum were identified in a previous work [B. J. Huang and T. M. Wu, Phys. Rev. E 79, 041105 (2009)]. The mass exponents and the singularity spectrum of the INMs are obtained by the box-size and system-size scalings under the typical average. The INM eigenvectors at a ME exhibit a multifractal nature and the multifractal INMs at each ME yield the same results in generalized fractal dimensions and singularity spectrum. Our results indicate that the singularity spectrum of the multifractal INMs agrees well with that of the Anderson model at the critical disorder. This good agreement provides numerical evidence for the universal multifractality at the localization-delocalization transition. For the multifractal INMs, the probability density function and the spatial correlation function of the squared vibrational amplitudes are also calculated. The relation between the probability density function and the singularity spectrum is examined numerically, so are the relations between the critical exponents of the spatial correlation function and the mass exponents of the multifractal INMs.
Multifractality of instantaneous normal modes at mobility edges
(2010-11-29)
Huang, B. J.
;
Wu, Ten-Ming
;
物理研究所
;
Institute of Physics
In terms of the multifractal analysis, we investigate the characteristics of the instantaneous normal modes (INMs) at two mobility edges (MEs) of a simple fluid, where the locations of the MEs in the INM spectrum were identified in a previous work [B. J. Huang and T. M. Wu, Phys. Rev. E 79, 041105 (2009)]. The mass exponents and the singularity spectrum of the INMs are obtained by the box-size and system-size scalings under the typical average. The INM eigenvectors at a ME exhibit a multifractal nature and the multifractal INMs at each ME yield the same results in generalized fractal dimensions and singularity spectrum. Our results indicate that the singularity spectrum of the multifractal INMs agrees well with that of the Anderson model at the critical disorder. This good agreement provides numerical evidence for the universal multifractality at the localization-delocalization transition. For the multifractal INMs, the probability density function and the spatial correlation function of the squared vibrational amplitudes are also calculated. The relation between the probability density function and the singularity spectrum is examined numerically, so are the relations between the critical exponents of the spatial correlation function and the mass exponents of the multifractal INMs.
Numerical studies for localization-delocalization transition in vibrational spectra
(2011-01-01)
Huang, B. J.
;
Wu, Ten-Ming
;
物理研究所
;
Institute of Physics
By investigating the localization-delocalization transition (LDT) in the instantaneous-normal-mode spectrum of a simple fluid we compare two numerical methods the level-spacing statistics and the multifractal analysis, for determining the LDT in vibrational spectra Both methods are based on scale invariance at the transition Within numerical errors, our results of the two methods give a reasonable agreement on the location of the transition (C) 2010 Elsevier B V All rights reserved